\(\pi {}_ 1\) et \(d_ 2\). (French) Zbl 0548.55014

Legrand, A.

Homotopie algébrique et algèbre locale, Journ. Luminy/France 1982, Astérisque 113-114, 234-237 (1984).

Summary: [For the entire collection see Zbl 0535.00017.]
Given a bundle \(X\to E\to V\) with \(\pi_ 1(V)\) not zero. Besides the monodromy of local systems \(H_*(X)\) or \(\pi_*(X)\) associated to E and which appear in the \(E^ 2\)-terms of the Serre spectral sequence (or generalized Shih spectral sequence [see the author, Homotopie des espaces de sections (1982; Zbl 0535.55001)]) the differentials \(d_ 2\) of these spectral sequences bring us \(\pi_ 1(V)\) actions on \(H_*(X)\) or \(\pi_*(x)\). We explain here these actions.

MSC:

55R20	Spectral sequences and homology of fiber spaces in algebraic topology
55R05	Fiber spaces in algebraic topology
55T10	Serre spectral sequences
55N25	Homology with local coefficients, equivariant cohomology
18G40	Spectral sequences, hypercohomology
18G15	Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)

Keywords:

monodromy of local systems associated to a fibration; differentials of spectral sequences; Serre spectral sequence

Citations:

Zbl 0535.00017; Zbl 0535.55001